In this paper, the formulation of a new fractional modified explicit group (FMEG) iterative method in solving the two-dimensional time fractional diffusion equation (TFDE) is presented. The method is formulated using the five-point centred difference approximation on the 2h grid stencils. The new developed method is shown to have a better convergence rate due to its lower computational complexity compared to others existing fractional group methods. Numerical experimentations of this new method, show significant improvement in execution time over the other explicit methods of the same class which enhances the effectiveness of the proposed method.

1.
A.
Carpinteri
and
F.
Mainardi
,
Fractals and Fractional Calculus In Continuum Mechanics
(
Springer
,
2014
).
2.
A.
Chaves
,
Phys. Lett. A
239
(
1
),
13
16
(
1998
).
3.
S. G.
Samko
,
A. A.
Kilbas
and
O. I.
Marichev
,
Fractional Integrals and Derivatives Theory and Applications
(
Gordon and Breach
,
New York
,
1993
).
4.
A. A.
Kilbas
,
H. M.
Srivastava
and
J. J.
Trujillo
,
Theory and Applications of Fractional Differential Equations
. (
Elsevier Science Limited
,
2006
).
5.
M.
Basu
and
D. P.
Acharya
,
J. Appl. Math. Comput.
10
(
1-2
),
131
143
(
2002
).
6.
Q.
Huang
,
G.
Huang
and
H.
Zhan
,
Adv. Water Resour.
31
(
12
),
1578
1589
(
2008
).
7.
A.
Kadem
,
Y.
Luchko
and
D.
Baleanu
,
Rep. Math. Phys.
66
(
1
),
103
115
(
2010
).
8.
Y.-n.
Zhang
and
Z.-z.
Sun
,
J. Comput. Phys.
230
(
24
),
8713
8728
(
2011
).
9.
Y.
Luchko
and
R.
Gorenflo
,
Preprint series A08–98, Fachbereich Mathematik und Informatik
(
Freie Universitat Berlin
,
1998
).
10.
D. M.
Young
,
J. Approx. Theory.
5
(
2
),
137
148
(
1972
).
11.
W.
Hackbusch
,
Iterative Solution of Large Sparse Systems of Equations
. (
Springer
,
1994
).
12.
Y.
Saad
,
Iterative Methods for Sparse Linear Systems
. (
Siam
,
2003
).
13.
D. J.
Evans
,,
Int. J. Comput. Math.
17
(
1
),
81
108
(
1985
).
14.
D. J.
Evans
and
A. R.
Abdullah
,
Int. J. Comput. Math.
14
(
1
),
73
105
(
1983
).
15.
A.
Ibrahim
and
A. R.
Abdullah
,,
Int. J. Comput. Math.
58
(
3-4
),
253
263
(
1995
).
16.
D. J.
Evans
and
W. S.
Yousif
,,
Int. J. Comput. Math.
18
(
3-4
),
323
340
(
1986
).
17.
W. S.
Yousif
and
D. J.
Evans
,
Parallel Algorithms Appl.
7
(
1-2
),
53
71
(
1995
).
18.
M.
Othman
and
A. R.
Abdullah
,,
Int. J. Comput. Math.
76
(
2
),
203
217
(
2000
).
19.
N. H. M.
Ali
and
N. K.
Fu
, “
Modified Explicit Decoupled Group Method in the Solution of 2-D Elliptic PDEs
” in
Proceedings of the 12th WSEAS International Conference on Applied Mathematics
,
Cairo, Egypt
,
December 2007
, pp.
162
167
.
20.
N. H. M.
Ali
and
D. J.
Evans
,
Int. J. Comput. Math.
81
(
9
),
1163
1174
(
2004
).
21.
L. M.
Kew
and
N. H. M.
Ali
, “
Explicit group iterative methods for the solution of telegraph equations
” in
proceeding of the International Conference of Applied and Engineering Mathematics World Congress on Engineering
,
2010
, pp
1770
1775
.
22.
N. H. M.
Ali
and
L. M.
Kew
,
J. Comput. Phys.
231
(
20
),
6953
6968
(
2012
).
23.
A. T.
Balasim
and
N. H. M.
Ali
, “
Group iterative methods for the solution of two-dimensional time-fractional diffusion equation
AIP Conference Proceedings
1750
,
030003
(
2016
); doi: .
24.
A. T.
Balasim
and
N. H. M.
Ali
,
Indian J. Sci. Technol.
8
(
32
),
1
7
(
2015
).
25.
I.
Karatay
,
N.
Kale
and
S. R.
Bayramoglu
,
Fract. Calc. Appl. Anal.
16
(
4
),
892
910
(
2013
).
26.
M.
Cui
,
Numer. Algorithms
62
(
3
),
383
409
(
2013
).
This content is only available via PDF.
You do not currently have access to this content.